Week 4 was the first week where I felt the material went beyond revision for a significant number of those attending. In advance of the class I prepared a set of simultaneous equations and 2 quadratic equations (one that is easy to solve by eye and the other which required the formula). In a previous week I had noticed a student solving simultaneous equations by a quite laborious method and I had performed a magician's trick showing a small group an easier way to solve them. I intended to perform the same magic here. The second topic of the day was quadratic equations. These are a traditional scapegoat in mathematics, often cited when people express their hatred for the subject. I intended to present them as methodical to solve and not worthy of attention; certainly not hatred.
So this was my first time writing on a white board in a class since tutorials at university. Nerve-wracking!
4 students attended. One was well in advance of the lesson plan and content to work through the material and ask questions if needed. The other three knew each other and formed a nice little group I talked to collectively.
On simultaneous equations, they copied down my method and seemed pleased with it if not astonished.
They had bad memories of quadratic equations. I showed them the "by eye" one and explained this is often a problem point for teaching this subject. The lecturer will say "and we see obviously that.." and the students are lost if they can't see how to complete the square. I told them not to worry if they didn't see how to do it. I then showed them the second method. I showed them the second method would solve the "by eye" quadratic equations too and that it was not incorrect, simply overkill, to use the method where a solution was obvious. So I said don't worry if you can't see the trick, the second method will work.
Then they had a go at some problems themselves. They seemed capable and confident at applying these half-remembered techniques and all got on well.
They left early.
